1. Field of the Invention
The invention relates to a method for obtaining a model representative of a heterogeneous medium from indirect measurements obtained from outside the medium and other data, particularly a set of pinpoint data measured in situ.
The method of the invention may be suitable in very different fields depending on the type of transmission used for obtaining the images. It applies particularly in the geophysical field, and in particular for the processing of seismic data. For the needs of seismic prospecting by reflection, waves are transmitted from a seismic source. They propagate in the ground to be explored, and the reflections of these waves from the discontinuities of the sub-soil are picked up by a set of seismic sensors spaced apart along the sub-soil section to be studied. The signals recorded as a function of time are generally sampled in digitized form. By regular movement of the seismic source and the set of sensors and repetition of the transmission-reception cycles, a large number of seismic traces are recorded containing information about the sub-soil.
2. Description of the Prior Art
Different ways of processing the recordings by programmed digital computers have been systematically utilized to improve their readability. It is a question in particular of stacking recording traces by applying the so-called multiple coverage method to improve the signal-to-noise ratio, or the deconvolution and migration method, as is well known by specialists, to improve the vertical resolution and the horizontal resolution.
In particular, preserved amplitude processing makes it possible to eliminate all the phenomena which are not related to the reflectivity of the discontinuities under normal incidence. Thus, the processing section is representative of the geological interfaces, the amplitudes of the reflected waves then being substantially proportional to the reflection coefficients corresponding to the discontinuities of the sub-soil. After preserved amplitude processing, the seismic image therefore contains lithologic information.
The improved seismic sections which are obtained after such processing are then available for interpretation. It is a question of transforming each seismic section in time into a lithologic image of the sub-soil and, therefore, to estimate with sufficient accuracy the value of the acoustic impedance of the different layers of the sub-soil, namely the product of their density by the speed of propagation of the waves which propagate therein, whose discontinuities are responsible for the reflections.
The passage to a lithologic representation of the sub-soil better representing the seismic sections obtained is generally very delicate to solve. A conventional method, by a so-called mono-channel deconvolution and by forming pseudo acoustic impedance logs, makes it possible to obtain such inversion. It consists essentially, with the seismic excitation to the ground being previously estimated, in reconstituting from real seismograms the real distribution of the values of the acoustic impedance as a function of the depth measured during the propagation time. Such a method is described for example in an article entitled "Inversion of Seismograms and pseudo-velocity logs" in Geophysical Prospecting, vol 25, pp 231-250, 1977.
The validity of the results is checked against other data which is available from elsewhere. In general, information is available concerning the position of the interfaces and certain characteristics of the sub-soil, whether they result from prior interpretations or have been obtained otherwise by making well measurements (well logging, PSV, etc . . . ) in one or more boreholes passing through the part of the sub-soil studied, with different tools.
The results obtained by this type of method are not always satisfactory. They often reveal themselves irreconcilable with the results of well-logging measurements. The divergence of the results is generally attributed to the uncertainties of the exact form of the excitation transmitted to the sub-soil, to the considerable background noise disturbing the useful seismic signals and also to their relatively narrow frequency band. In addition, the solutions which can be found to the inversion problem are unstable. Very different impedance distributions may just as well explain the same seismic section. The task of the interpreter who must derive a geological model from the distribution of the impedance values obtained by these inversions, by reconciling it with the different data known from elsewhere, is therefore delicate. It is also found in practice that the lithologic model obtained may be questioned.
A known approach for overcoming the inaccuracies of a model, consists in improving it by successive steps. From an initial model chosen a priori from data resulting from interpretations and well-logging, and at this stage still largely hypothetical, synthetic seismograms are calculated of the model, and they are compared with actual seismograms. Since the differences noted represent the imperfection of the model, the latter is modified. This cycle of constructing synthetic seismograms and comparison is repeated, and the variations applied to the basic model are progressively selected which lead to a reduction of the differences so as to approximate as much as possible the actual seismograms obtained.
It is also known to automate the above process by searching for the acoustic impedance distributions, such that the synthetic seismograms are adjusted as well as possible to the seismic recordings. Such approaches using a mono-channel are described, for example, by Bamberger et al. in Geophysics vol 47, pp 757-770, May 1982, or by Oldenberg et al., in Proceedings of the IEEE, special issue on Seismic Inversion, Mar. 1986.
Obtaining an impedance section which is compatible with the geological information makes it necessary to impose a lateral correlation on the results and so to find solutions suitable in a plane, rather than a series of independent solutions by considering separately the inversion of the different traces. Such processing is multi-channel. Depending on the parameterization method of the lithologic model, very different resolution methods are adopted.
The interval (O,X) which corresponds to the length of the seismic profile which it is desired to interpret, having been divided into a succession of disjointed intervals between checking points, the model may be parametered by the geometry of the layers and assuming that the impedance is a constant function in depth inside each layer and continues with a linear variation at x inside each of said intervals. Such a method is described for example in the U.S. Pat. No. 4,679,174.
This method of parameterization is interesting if it makes it possible to reduce the number of parameters to be processed, i.e. if the thickness of the different layers and the disjointed intervals are not chosen too small. However, in this case, the parameterization will not reflect reality, since the distribution of the acoustic impedance values inside a geological layer that is generally much more complex.
The method of the invention makes it possible to obtain an optimum model in at least two dimensions representing the variations of at least one physical parameter of a heterogeneous medium such as the sub-soil, responsible for the reflections undergone by waves transmitted into the sub-soil, the model agreeing as well as possible with recordings of signals received by a set of sensors disposed outside the medium in response to the waves reflected from the medium, with a value of said physical parameter chosen at at least one point, obtained following measurements or evaluations and with other information relating to the desired type of heterogeneity. It comprises
the construction of a reference model in which the values of the physical parameter are adapted to the chosen values and to the information relating to the heterogeneities,
the construction of synthetic recordings representing the response of the model to the waves transmitted from outside, and
the construction of the optimum model which makes possible an adjustment of the synthetic recordings with respect to the recordings of received signals.